The number 3504
3504 is a composite number with 20 divisors. Its prime factorisation is × 3 × 73. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584 … 3504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3504: a Harshad number: divisible by its digit sum 12.
- 2
3504 is composite. Its prime factorisation is
- 3
The divisors add up to 9176; without 3504 itself that is 5672, so 3504 is abundant (5672 is more than 3504). Euler's totient φ(3504) = 1152 numbers up to 3504 share no factor with it.
- 4
The digits of 3504 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3504 = 2^{4} \times 3 \times 73 \]3504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 9176 |
| Euler totient φ(n) | 1152 |
| Square | 12278016 |
| Cube | 43022168064 |
| Square root | 59.194594 (= 4√219) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 56 |
| Scientific notation | 3.504 × |
3504 in other forms
| Form | Value |
|---|---|
| In words | three thousand five hundred and four |
| Roman numerals | MMMDIV |
| Binary (base 2) | 110110110000 |
| Octal (base 8) | 6660 |
| Hexadecimal (base 16) | DB0 |
| Base 3 | 11210210 |
| As time | 3504 seconds = 58 min 24 s |
Is 3504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3504 ÷ 2 = 1752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3504 ÷ 3 = 1168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3504 ÷ 4 = 876) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3504 ÷ 6 = 584) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (3504 ÷ 8 = 438) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3504 ÷ 12 = 292) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3504 a prime number?
No. 3504 = × 3 × 73, so it is divisible by 2.
What are the factors of 3504?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584, 876, 1168, 1752, 3504.
What is 3504 in binary?
110110110000 (hexadecimal DB0, octal 6660).
What is the square root of 3504?
About 59.1946, exactly 4√219.
What is 3504 in Roman numerals?
MMMDIV.
Is 3504 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 3504?
3504 is a Harshad number: divisible by its digit sum 12.